On the limits of validity of effective dispersion models for bulk reactions

Dispersion models containing a single effective dispersion coefficient have been extensively used in the literature to predict the performance of chem ical reactors. In recent years, there is considerable debate on whether the effective dispersion relations determined in the absence of reaction are a lso valid in the presence of a reaction, especially for the case of bulk re actions. We examine this problem in some detail and show that for the two m ost commonly used effective dispersion models (axial dispersion and tanks-i n-series or cell model), the widely used relationship N = Pe/2, (Pe>> I, N = number of cells and Pe = Peclet number), derived in the absence of a reac tion, also holds for all slow reactions characterized by 0 less than or equ al to Da\f'(cN)\ < Pe(2/3). Here, Da is the Damkohler number and f'(c(N)) i s the derivative of the normalized reaction rate at the exit concentration c(N) of the cell model. For Da values exceeding this upper bound (fast reac tion regime), the model predictions diverge, or equivalently, the effective dispersion coefficient concept is not valid. We show that the same result applies for transient behavior of the discrete and continuous (PDE) models provided Da is replaced by <root>Da(2) + omega (2), where omega is the dime nsionless forcing frequency. We also derive similar bounds for two other co mmonly used dispersion models, namely, the recycle and interphase resistanc e models. A formula for choosing the mesh size for fast reactions so that t he discrete and continuous models have the same qualitative features is als o presented. The analytical results derived for linear reactions are valida ted for nonlinear kinetics using numerical simulations. Some new results an d comparisons are also presented at the other extreme of near perfect mixin g. (C) 2000 Elsevier Science Ltd. All rights reserved.